A textbook of mass 2.00kg rests on a frictionless, horizontal surface. A cord at

Question

A textbook of mass 2.00kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.200m , to a hanging book with mass 2.91kg . The system is released from rest, and the books are observed to move a distance 1.19m over a time interval of 0.850s .

Part A

What is the tension in the part of the cord attached to the textbook?

Part B

What is the tension in the part of the cord attached to the book?

Take the free fall acceleration to be g = 9.80m/s2 .

Part C

What is the moment of inertia of the pulley about its rotation axis?

Take the free fall acceleration to be g = 9.80m/s2 .

Explanation / Answer

you can get the acceleration from d = 1/2 a t^2 where d and t are given and you solve for a

1.19 = 0.5*a* 0.85^2

a= 0.3035

then T1 = 4.0 a

T1= 0.6071 N

and T2 = 5.0 (g - a)

T2= 0.8834 N

C)

the torque on the pulley is Q = r (T2 - T1) and is equal to I (dw/dt)

where I is the moment of inertia and dw/dt is the angular acceleration.

The angular acceleration is related to the linear acceleration by dw/dt = a/r

I (a/r) = r (T2 - T1)

I (0.3035/0.100) = 0.100(0.8834 - 0.6071)

I = 0.0910

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